A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

Site-diluted quantum Heisenberg spin model applied to the magnetic properties of Fe–Al disordered alloys

In this work we present a theoretical study of the magnetic behavior of disordered Fe–Al alloys on the basis of a simple-diluted quantum Heisenberg spin model with the assumption that the exchange interaction J depends on the Al concentration q. We calculated the critical temperature and exponents through the mean field renormalization group method. An acceptable fit to the experimental phase diagram for Al concentration in the range 0.30q0.45 is obtained.     

All local classical symmetries in Hamiltonian mechanics

Using the formalism of symplectic group actions and coadjoint orbits, we give a complete list of all classical simple Lie algebras which are local symmetries for a given Hamiltonian vector field.     

The trace of totally positive algebraic integers

For all totally positive algebraic numbers except a finite number of explicit exceptions, the following inequality holds:

\max(1.780022,1.66+\alpha_1), \end{displaymath}">

where is the degree of and its conjugates. This improves previous results of Smyth, Flammang and Rhin.

     

Ultrafast dynamics of delocalized and localized electrons in carbon nanotubes

We report on the dynamics of the dielectric function of single-wall carbon nanotubes in the 10-30 THz frequency range after ultrafast laser excitation. The absence of a distinct free-carrier response is attributed to the photogeneration of strongly bound excitons in the tubes with large energy gaps. We find a feature of enhanced transmission caused by the blocking of optical transitions in small-gap tubes. The rapid decay of a featureless background with pronounced dichroism is associated with the increased absorption of spatially localized charge carriers before thermalization is completed.     

Electrostatic potential: A new approach for some mixed boundary value problems

A new approach to the solution of problems of electrostatics, some of them with mixed boundary conditions, is presented. The proposed scheme can be used in cases were we have a formal solution in the form of a series in Legendre polynomials and the boundary or matching conditions are given not on the whole interval (0, π) of the polar variable, θ, but only over the interval (0, π/2) or (π/2, π). Truncation of the series after the Nth term and the projection on the subspace generated by the set of the first N even (or odd) Legendre polynomials allows us to determine the unknown coefficients of the approximate solution. The results show rapid convergence toward the exact values as we increase the number of terms, N, included in the approximate solutions. The procedure allows to solve approximately some problems whose exact solutions, we believe, are not yet known.     

New palladium (II) complexes containing phosphine‐nitrogen ligands and their use as catalysts in aminocarbonylation reaction

Aminocarbonylation of aryl halides, homogeneously catalysed by palladium, is an efficient method that can be employed for obtaining amides for pharmaceutical and synthetic applications. In this work, palladium (II) complexes containing P^N ligands were studied as catalysts in the aminocarbonylation of iodobenzene in the presence of diethylamine. Two types of systems were used: a palladium (II) complex formed in situ; and one prepared prior to the catalytic reaction. In general, the palladium complexes studied achieved high conversions in an average reaction time of less than 2 hr, which is less than that for the standard system (Pd (II)/PPh₃) used. The pre‐synthesized complexes were faster than their in situ counterparts, as the latter require an induction time to form the Pd/P^N species. The structure and electronic properties of the ligand P^N can influence both the activity and the selectivity of the reaction, stabilizing the acyl‐palladium intermediates formed in a better manner.